MATHS IN ENGLISH
CONTENT AND LANGUAGE INTEGRATED LEARNING
| Exercises | Solutions |
1. REAL NUMBERS
1.1 Basic operations on numbers
1.2 Natural numbers and divisibility tests
1.3 Integers and rational numbers
1.4 Irrational numbers
1.5 Decimal expansion of a real number
1.6 Square root
1.7 Cube root
1.8 Radicals
1.9 Powers with integer exponents
1.10 Powers with rational exponents
1.11 Logarithms and their properties
1.12 Per cent, per mile
1.13 Percentages and compound interests
2. THE LANGUAGE OF MATHEMATICS
2.1 Set, element, subset
2.2 Defining sets
2.3 Operations on sets
2.4 Intervals
2.5 Solving inequalities
2.6 Taking out a common mnomial
2.7 Multiplying algerbaic sums
2.8 Short multiplication formulas
2.9 Application of algebraic manipulation
2.10 Absolute value
2.11 Complementary issus
3 SYSTEM OF EQUATIONS
3.1 Systems of equations
3.2 Substitution method of solving systems of equations
3.3 Elimination method of solving systems of equations
3.4 Application of systems of equations
4. FUNCTIONS
4.1 Concept of a function
4.2 Graph of functions
4.3 Monotonicity of functions
4.4 Properties of function reading from graphs
4.5 Vectors in the XY-plane
4.6 Shifting a graph along the X and Y axis
4.7 Reflections of graphs
4.8 Inverse proportionality
4.9 Complementary issues
5. LINEAR FUNCTION
5.1 Graph of a linear function
5.2 Properties of a linear function
5.3 Equations of a line on a plane
5.4 The gradient of a line
5.5 Parallel and perpendicular lines
5.6 Geometric interpretation o a system of linear equations
5.7 Aplications of linear functions
5.8 Complementary issues
6. PLANIMETRY
6.1 Internal angels in a triangle
6.2 Congruent triangles
6.3 Basic Proportionality Theorem (Thales' Theorem)
6.4 Similar polygons
6.5 Similar triangles. Areas of similar triangles
6.6 Angle bisector theorem
6.7 Complementary issues
7. QUADRATIC FUNCTION
7.1 Quadratic monomial
7.2 Different forms of a quadratic function
7.3 Properties of a quadratic function
7.4 Quadratic equations
7.5 Quadratic inequalities
7.6 Maximum and minimum value of a quadratic function
7.7 Applications of a quadratic function
8. POLYNOMIALS
8.1 Definition of a polynomial of a real variable
8.2 Operations on polynomials
8.3 Short multiplication formulas (2)
8.4 Factorizing polynomials
8.5 Polynomial equations
8.6 Bezout Theorem
8.7 Integer and rational roots of poynomials
8.8 Application of polynomials
8.9 Comlementary issues
9. RATIONAL FUNCTIONS
9.1 Inverse proportionality functions and and their properties
9.2 Operations on rational expressions
9.3 Rational equations
9.4 The domain of a function. Rational function.
9.5 Equations and inequalities with absolute value
9.6 Applications of rational equations
10.TRIGONOMETRY
10.1 Right angeled triangles
10.2 Trigonometric functions of an acute angle
10.3 Solving right triangles
10.4 Trigonometric identities
10.5 Trigonometric functions of a convex angle
10.6 Area of a triangles
10.7 Area of a quadrilateral
10.8 Complementary issues
11. PLANIMETRY II
11.1 A cirlce and a disc
11.2 A line and a cirlce
11.3 Angles in a circle
11.4 Circumscribed and inscribed triangles
11.5 Reagular polygons
11.6 The Sine Rule
11.7 The Cosine Rule
12. EXPONENTIAL AND LOGARITHMIC FUNCTIONS
12.1 Powers with rational exponents - revision
12.2 Powers with real exponents
12.3 The exponential function
12.4 Graph transformations of exponential functions
12.5 Logarithms - revision
12.6 Laws of logarithms
12.7 Logarithmic function
12.8 Graph transformations of logarithmitc function
12.9 Applications of exponential and logarithmic functions
13. ANALITYC GEOMETRY
13.1 Distance on the Cartesian plane
14. SEQUENCES
14.1
15. STATISTICS
15.1 Arithmetic mean
16. PROBABILITY
16.1 Multiplication Rule
16.2 Permutations
16.3 Variation without repetition. Variations with repetitions
16.4 Addition Rule
16.5 Random events
16.6 Classical probability
16.7 Complementary issues
17 STEREOMETRY
17.1
18. MATHEMATICAL PROOFS
18.1 Proofs in algebra
18.2 Proofs in geometry
XLO im. Stefana Banach w Toruniu
2024